Summary of Skills

Unit 1: Introduction to Multiplication and Division

Math

Determine the unknown whole number in a multiplication or division equation relating three whole numbers

Fluently multiply and divide within 100

Identify arithmetic patterns, and explain them using properties of operations

Identify equal groups

Interpret and create arrays that model multiplication

Interpret products of whole numbers (for example, interpret 5 &#x00d7; 7 as the total number of objects in 5 groups of 7 objects each)

Interpret whole-number quotients of whole numbers (for example, interpret 56 &#x00f7; 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each)

Know from memory all products of two one-digit numbers

Skip count

Understand division as an unknown-factor problem

Use arrays to create addition sentences

Use equal groups to model multiplication

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities

Use repeated addition and number lines to model multiplication

Use the language of multiplication

Unit 2: Place Value

Math

Assess the reasonableness of answers using mental computation and estimation strategies including rounding

Count to 10,000

Count to 10,000

Fluently add and subtract beyond 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction

Fluently add and subtract beyond 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction

Know from memory all products of two one-digit numbers

Read and write numbers to 10,000 using base-10 numerals, number names, and expanded form

Read, write, and skip count to 1000

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones

Use place value understanding to round whole numbers to the nearest 10 or 100

Use place value understanding to round whole numbers to the nearest 10 or 100

Unit 3: Measurement

Math

Add, subtract, multiply, or divide to solve one-step word problems involving weights or volumes that are given in the same units

Measure and estimate liquid volumes (capacities) using standard units

Measure and estimate liquid volumes and weights of objects using standard units

Measure and estimate liquid volumes using standard units

Measure and estimate weight using standard units

Measure and estimate weights of objects using standard units

Solve word problems involving addition and subtraction of time intervals in minutes

Tell and write time to the nearest minute

Tell and write time to the nearest minute and measure time intervals in minutes

Tell and write time to the nearest minute and measure time intervals in minutes

Tell, show, and talk about time to 5 minutes

Unit 4: Multiplication and Division II

Math

Apply properties of operations as strategies to multiply and divide

Determine the unknown whole number in a multiplication or division equation relating three whole numbers

Fluently multiply and divide within 100

Fluently multiply and divide within 100

Identify arithmetic patterns

Interpret products of whole numbers, e.g., interpret 5 &#x00d7; 7 as the total number of objects in 5 groups of 7 objects each

Interpret whole-number quotients of whole numbers, e.g., interpret 56 &#x00f7; 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each

Multiply one-digit whole numbers by multiples of 10 in the range 10-90

Multiply one-digit whole numbers by multiples of 10 in the range 10-90

Solve two-step word problems using the four operations

Solve two-step word problems using the four operations

Understand division as an unknown-factor problem

Use multiplication and division to solve word problems

Use multiplication and division within 100 to solve word problems

Use multiplication and division within 100 to solve word problems

Unit 5: Area and Perimeter

Math

Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts

Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems

Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems

Name, describe, and create polygons

Recognize area as an attribute of plane figures and understand concepts of area measurement

Relate area to the operations of multiplication and addition

Solve real world and mathematical problems involving perimeters of polygons

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths and finding an unknown side length

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters

Understand that a square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area

Unit 6: Fractions

Math

Compare two fractions with the same numerator or the same denominator

Compare two fractions with the same numerator or the same denominator by reasoning about their size

Record the results of comparisons with the symbols &#x003e;, =, or &#x003c;, and justify the conclusions

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line

Show fractional parts of shapes

Understand a fraction <i>b</i> as the quantity formed by 1 part when a whole is partitioned into <i>b</i> equal parts; understand a fraction <i>a/b</i> as the quantity formed by <i>a</i> parts of size 1/<i>b</i>

Understand a fraction 1/<i>b</i> as the quantity formed by 1 part when a whole is partitioned into <i>b</i> equal parts; understand a fraction <i>a/b</i> as the quantity formed by <i>&#x003c;</i>i&#x003e;a</i> parts of size 1/<i>b</i>

Understand a fraction 1/<i>b</i> as the quantity formed by 1 part when a whole is partitioned into <i>b</i> equal parts; understand a fraction <i>a/b</i> as the quantity formed by <i>a</i> parts of size 1/<i>b</i>

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts

Understand a fraction 1/B as the quantity formed by 1 part when a whole is partitioned into B equal parts; understand a fraction A/B as the quantity formed by A parts of size 1/B

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b

Understand a fraction a/b as teg quantity formed by a parts of size 1/b

Understand a fraction a/b as the quantity formed by a parts of size 1/b

Understand a fraction as a number on the number line; represent fractions on a number line diagram

Understand two fractions as equivalent (equal) if they are the same size